When did the Church come up with the doctrine that each species contains both the body and the blood of Christ?

The Church has always taught that each species contains both the body and blood of Christ. This dogma was reaffirmed at the Council of Trent:

Because Christ our Redeemer said that it was truly his body that he was offering under the species of bread, it has always been the conviction of the Church of God, and this holy Council now declares again, that by the consecration of the bread and wine there takes place a change of the whole substance of the bread into the substance of the body of Christ our Lord and of the whole substance of the wine into the substance of his blood. This change the holy Catholic Church has fittingly and properly called transubstantiation. (Denzinger-Schönmetzer, 1642)

The document “Norms for the Distribution and Reception of Holy Communion Under Both Kinds in the Dioceses of the United States of America” states:

It should never be construed, therefore, that Communion under the form of bread alone or Communion under the form of wine alone is somehow an incomplete act or that Christ is not fully present to the communicant. The Church’s unchanging teaching from the time of the Fathers through the ages—notably in the ecumenical councils of Lateran IV, Constance, Florence, Trent, and Vatican II—has witnessed to a constant unity of faith in the presence of Christ in both elements.

Even in the earliest days of the Church’s life, when Communion under both species was the norm, there were always instances when the Eucharist was received under only the form of bread or wine. . . . Thus, the Church has always taught the doctrine of concomitance, by which we know that under each species alone, the whole Christ is sacramentally present and we receive all the fruit of Eucharistic grace. (15)